Saying something is “non-physical” is often taken as a negative definition: it tells us what it is not rather than what it is.
Without clear positive criteria or empirical markers, it’s difficult to say what the non-physical actually is beyond abstract qualities. So how have dualists posited a positive criteria for what counts as non physical?
Some dualists hold that the mind and/or mental properties are non-physical.
They can positively describe mental properties in intentional, mental, or phenomenological terms.
For example, they can say that "feeling sad", "seeing red", and "thinking about math" positively describe certain non-physical mental properties.
You can't very well have a positive description of a negative quality. That's like asking if there are positive qualities to describe "not an American" or "not a canine".
Non-physicalists do, however describe positive properties for a variety of categories of object that they say is non-physical.
It's useful to ask what dualists think are the two kinds of thing that reality can be divided into - but it won't admit a single correct answer without further specification: there are lots of different dualisms, just like there are lots of different monisms.
It's not useful to stake out your position on a set of terms (i.e. all is physical), and then ask your interlocutor to define the terms for you. Letting your interlocutor define the terms on which you have established your position is the exact same thing as having no position at all and agreeing with whatever your interlocutor says.
For example:
As a dualist given authority to define the "non-physical" that physicalists don't believe in:
Figuring out what something IS -- can be quite a challenge. We still don't know what gravity is, despite living with it for millennia.
The challenge to non-physicalists to define the non-physical is one that cannot be met, as Hempel's Dilemma spells out. One cannot define "physical" in a way that prohibits the things that physicalists want to deny (souls, spirits, Gods, causal minds) without the definition being either useless/untestable, or false.
A good way to approach this question is to start with epistemology -- how does one develop knowledge? Definitions are a poor way to develop knowledge. Much better is observation, then model fitting. This is what empiricism does and is something most physicalists claim to ascribe to. So -- what can we learn by considering empiricism?
Karl Popper's 3 worlds considers the best model of our world is that here are three types of things, those with space and time properties (matter, mostly), those with just time properties (experiences, consciousness), and those with neither space nor time properties (abstractions).
If the physical is matter, then in Popper's terms, the non-physical would be worlds 2 and 3.
As with the Hempel's Dilemma critique of the definitions of physicalism/physical -- definitions of Popper's 3 worlds will be difficult to nail down with precision. Treat them as a useful approximation.
How do dualists define the non physical?
From the IEP on Dualism and Mind:
Dualists commonly argue for the distinction of mind and matter by employing Leibniz’s Law of Identity, according to which two things are identical if, and only if, they simultaneously share exactly the same qualities. The dualist then attempts to identify attributes of mind that are lacked by matter (such as privacy or intentionality) or vice versa (such as having a certain temperature or electrical charge).
The Wikipedia page states that for x to be physical it has to be either matter or energy. Some add that even fields are physical. If an x is not any of these then it's nonphysical. That's what the definition of physical informs us of, but the utility of such a definition for inquiry is questionable. Descartes describes the mind as res cogitans, it is to him something, a substance, that lacks the physical quality of extension.
Descartes explicitly defined the equivalent of non-physical substances as res cogitans vs. res extensa. A Kantian adjustment was assimilating experience of personal identity to the sense of time as distinct from space, and Kant seems to slightly concur with Descartes that transcendental apperception is simple in some way that spatially divisible objects are not (but Kant looked to the possibility of neutral monism as a way to harmonize the space-resistant properties of apperception and the space-dependent properties of physical matter).
An advanced modal account would differentiate between objects entering into transworld identity vs. counterpart relations. We might say that blobs of matter are only counterparts of blobs of matter in other worlds, not transworld-identical to those blobs, but that mental substances proper (not as quantities of "stuff" but in the original Aristotelian sense of primary subjecthood for predication theory) are transworld-identical to things in other possible worlds. It is really us, as transmaterial persons, who can choose between the possibilities encoded by alternative worlds. Whether there are kinesthesia-like "perceptions" or "sensations" of free will/choice is not clear (we do have "experience" resisting various urges and emotions, and there might not be one other urge/emotion overpowering the others besides the paradoxical desire for hard free will itself (Kant's "acting under the idea of freedom"), but if such a desire is a cause of action, is it predictable what actions it causes?). (Cf. the question of modal perception.)
Or one might cite Gödel to the effect that we might have an entirely other mode of non-discursive awareness that engages with spacetime-free objects. It is not absolutely clear that Kant has a sharp dichotomy between human empirical intuition and divine intellectual intuition, because he says that the dimensionality of empirical intuition is analytically contingent, but a being with empirical intuition in e.g. 24 spacetime dimensions would be neither as limited as we are nor as unlimited as the agent of intellectual intuition, and so we can imagine infinitely many kinds of intuition beyond ours but before God's. Was Gödel committed to us having intellectual intuition of mathematical objects or rather just some special alternative class of technically empirical intuition? In fact, he was not so averse to talking about empirical learning in mathematics, e.g. with his whole analogy between extrinsic justification of set-theory axioms and inductive reasoning. (See also here.)
In short, the viability of multiple types of substances is caught up with the question of the multiplicity of intuition. From a certain (and extreme!) nominalist perspective, no set of intuitions is actually closed by abstract type, so in a way, seeing and hearing already count as representative of multiple possible substances (and no one event of sight is the same as another by abstract/general type, so even any two seeings might count as representative of two fundamentally different substances).
Physical is usually considered something, knowledge about which is accessible via scientific method.
