The oil cooler on which the oil filter mounts is a known weak spot on these cars. (They have failed on my 1996 A4, my wife's 2001 Passat, and my elder son's 2002 A4.) Because oil pressure is higher than coolant pressure, cross-contamination from oil into coolant is more common than the reverse, but either could happen.
You definitely want to inspect the bottom of the cap on your coolant recovery tank, as well as the color of your coolant. Brown, discolored coolant and/or residue on the underside of the cap indicate that oil is getting into the cooling system. Again, if you are lucky, it is an easily replaced $50 oil cooler; if not, it is a head gasket or a cracked head, as others have mentioned in this thread.