Most cemeteries do allow for cremated remains to be interred in the same grave of a full burial. There are fees involved such as the cost of purchasing a “2nd right of interment” (the right to bury a 2nd set of remains in the same space), as well as the fee to do the burial.
I would recommend that you contact the catholic cemetery and find out what all they require for this. There may be paperwork to do as well. For example – if you have any siblings that would be also be next of kin to your parents, they may need to get permission from them to allow the 2nd burial in the grave.