Rothschild doesn't consider your q to be a propositional assertion, but rather an expression of an attitude towards a proposition. He is using proposition here in a limited sense of a statement that has truth conditions, so "it might be the case that p" is not, for him, a proposition itself but a doxastic property of our attitude towards p.
To put this in a broader context, Rothschild is addressing the question of whether conditionals can be said to express propositions at all. On the suppositional account of conditionals, which is held by Ernest Adams, Dorothy Edgington and Jonathan Bennett, conditionals are not propositions, because they do not have truth conditions. Rather, they serve as devices to introduce a supposition and make an assertion within the context of that supposition.
Rothschild is sympathetic to the arguments that support the suppositionalist account, but he is trying to steer round them and argue for a propositional account of conditionals under which they can be understood as quantificational restrictors. A version of this position is also defended by Angelika Kratzer.