It is very popular among philosophers to "overcome" the divide between idealism and materialism by dissolving the distinction, i.e. "embedding" both ideality and matter into something more fundamental, which they are then reconstructed as extreme cases of (equally popular is dissolving the distinction between subject and object). The idea is not to put a third option next to ideality and matter, but, to use Hegels's word, "sublate" them into a higher unity.
One of the first was perhaps Plotinus, the father of neo-Platonism, whose One precedes existence itself (and hence is neither ideal nor certainly material), and then "emanates" the world out of itself while remaining unchanged. This egress proceeds in decreasing phases of lucidity. The upper emanated echelons are ideas and ideal beings, while the lowest phase before the non-being is the inert matter. If this sounds familiar it should, Augustine and through him the Christian theology, was deeply influenced by Plotinus.
Spinoza accomplished it by dissolving God in nature understood as "being absolutely infinite, i.e., a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence... Extension is an attribute of God, or God is an extended thing". Material and ideal are simply different attributes perceived by us as disjoint due to a limited perspectives. What we perceive in the "physical progression" as causally moving matter is in the "logical progression" a chain of inferences about ideas (hard determinism follows). Spinoza was very optimistic, he believed in the "third kind of knowledge", unified grasping of the substance as a whole in all of its attributes. He claimed, the only one to do so in the West, that “the human Mind has an adequate knowledge of God's eternal and infinite essence”. In the East, similar ideas emerged much earlier in Vedic philosophies and religions, under the motto that Atman (soul) is identical to Brahman (world).
Kant, Husserl, Heidegger and so on would not stand to be classified so crudely as materialists, idealists or dualists either (they are also the ones who, along with Schelling and Hegel, claimed to dissolve the subject/object distinction). They redefine "matter" and "ideality" radically, both are treated not as constituents of reality, but more or less as different aspects of cognition. E.g. to Kant matter is the "blind" stuff of outer sensibility, without which ideas (concepts) are "empty". It makes little sense to talk about ideal and material separately, and no sense at all to apply such predicates to supersensible "things in themselves". Husserl's position is similar, he characterizes ideal and material as abstracted extremes of perceptual spectrum, with perception in its fullness fusing and surpassing both. Existentialists' "existence precedes essence" leads to a similar view.