A bit more 'quick and dirty' solution you could try making a BindingList<Object> from the other two BindingLists.
Now when you deserialize it just do something like the following:
BindingList<object> objBl = (BindingList<object>)serializer.Deserialize(strm);
BindingList<myObj1> bl1 = new BindingList<myObj1>(objBl.OfType<myObj1>().ToList());
BindingList<myObj2> bl2 = new BindingList<myObj2>(objBl.OfType<myObj2>().ToList());
Should work, but as I said it's the quick and dirty solution.
I'd take SAKryukov's solution, but since I understand that's not the easiest solution (but best by far) I wanted to give you an easier solution.
Beware though, this might help you out in the short run, but it will come back and bite you later on :)