I don't know about the house thing. Perhaps someone else reading this thread will have more insight. However, from what I've read elsewhere, it seems there may be no way of knowing or deducing what his involvement with the house means if it means anything at all. He may not even know.
At least your H doesn't appear to be rushing to the D like my W is. Right now she can't seem to get it quick enough. You, however, may have a small opportunity to do some kinds of work that aren't an option for me at this point.
Are you and H living under the same roof or has he/you moved out? Any joint or individual counseling? Has he filed (it's always easier to talk about it than actually do it)?
Just some questions that might help someone else give you more insight than I can supply with my limited experience. I feel confident sharing what I've gone through and what's helped me to this point...but I'm reluctant to offer "advice" in other areas where my comments would be more akin to speculation.
