I am on probation and he is making parole. Can we get married in the state of Mississippi, where we both reside?

Not if probastion and parole are because of the same crime, in fact you most likely can not even see each other.

But just to see each other, you will have to have probation officers permission and he will have to get PO permission.

To marry you will both need permission from each of yours PO.

One of the restrictions is normally no association with other people on parole or probation