It is common nowadays to distinguish substance from property dualism. No major philosopher has advocated substance dualism since Descartes himself, but a large number of philosophers have advocated property dualism. This is a view which classifies the properties of objects as being of two kinds, physical and mental, while maintaining monism or quietism about the ultimate nature of substance.
Advocates of this view include Donald Davidson (his theory of Anomalous Monism), Richard Rorty (non-reductive physicalsim), Wilfrid Sellars (in his A Semantical Solution to the Mind Body Problem). They have all argued that there are events which simultaneously have both physical and mental properties, and that these properties are not reducable to one another. All have asserted the ontological identity of properties without asserting epistemological identity. Like Frege's way of differentiating the meaning of two co-referring terms by attributing to each a distinct 'sense', they are suggesting that physical attributes and mental attributes ultimately belong to same entities, but that the very notion of a property or attribute is inseparable from human understanding, i.e. it is epistemic in nature, and hence arises the mind-body problem.
Indeed, of the main schools of thought in philosophy of mind in the last few decades-identity theory (type and token), functionalism and a so-called 'new materialism'- all of them have asserted ontological identity of physical and mental properties while respecting the epistemological irreducibility of physical and mental predicates.
The majority of philosophers asserting views of these kinds would probably accept being called 'non-reductive materialists', i.e. mental properties are physical properties in some metaphysical but conceptually irreducible sense. The mental-physical relation is one of identity for them, so they do not give ontological priority to mind or matter, yet they call themselves 'materialists'. That is because while all objects and events have physical properties, only some of them have mental properties. In that sense, everything is physical, but not everything is mental.
Many others have rejected this thesis, and the label 'materialism', and rejected the metaphysical or ontological identity of mental/physical properties, e.g. Jackson, Sprigge, Honderdich. A good summary is in Chalmers 1996 p. 166+. Rejecting materialism implies a strong dualism about properties without saying anything about the ultimate nature of substance, or that every event is physical. The position is close to that of Descartes. Others have adopted a quietism where the ultimate nature of things is unstated (e.g. the so-called 'New Mysterians' such as Colin McGinn actually say the mind-body relationship is ultimately unknowable to the human mind).
Most philosophers would agree not all states or events have mental properties (i.e. some events are purely physical), only some do. Some of these mental events we would characterise as thoughts, having conceptual properties such as an inferential role or a logical syntax. Other mental events are not thoughts, e.g. pain. But for materialist philosophers, all mental events are identical to physical events, i.e. the same event under a different description (e.g. pain is the firing of C-fibres). The key points of interest for all is the conceptual and metaphysical relations between the mental and physical properties of such events. The metaphysical level is usually taken as identity, while the conceptual level is usually characterised as a mutual dependence relation, which is given the name 'supervenience' (Jaegwon Kim writes extensively on this relation).
I tend to think that classifying properties in a dualistic way is in a sense fundamental to our way of thinking about the world, and though it leads to paradox (the mind-body problem), we have no better schema, idealism and materialism notwithstanding.
Tyler Burges' paper Philosophy of Mind: 1950-2000 in his book Foundations of Mind, Philosophical Essays vol. 2 provides an excellent summary of recent philosophy of mind.