If we share a house with another couple but the man passed away and his wife was not on the mortgage, who owns the house?

You are here admitting that they owned the house together and the mortgage is not really my concnern here.  Is she on the deed to the property?  Then she owns the house too and depending on how the deed reads, she owns the entire half that they owned togather.  Now, all the documents that you mention here do not necessarilt determine ownership.  When they purchased the car, etc., matters.  Also, you can not cut your spouse out of your estate so even if the assets were deemed to have to be probated she probably gets a statutory share.  Speak with a lawyer.  Good luck.