Yes if you have a joint tenancy, then on his death you get the whole lot
Also his remarriage does not change the tenancy { remarriage does not sever the jointure}
BUT as bednobs said, you should check / verify
The divorce papers should have specified how the properties were to be divided.
IS it really the case, you only have a verbal agreement as to how property was divided ? From what you say, you seem to have checked that the ownership is recorded at the LR as joint.