Dear Monica:

I moved your question to this forum since it is not really about liturgy.

Concerning your question, marriage between a Catholic and a non-baptized person (called a "Disparity of Cult") is invalid in-and-of-itself and cannot be Sacramental. It is possible to get permission to marry a non-Christian, however. In order for your son to stay in good standing with the Church, he will have to ask the Bishop for a dispensation to get married to a Buddhist. The local pastor should help you son do this, or do it for him.

As for ceremonies, in order to permit this marriage your son and his intended will have to have a Catholic Wedding, which means that the exchange of vows must be in a Catholic ceremony, usually in a Catholic parish, though permission can be granted to another suitable place.

It is not permitted to have a second ceremony in which vows are exchanged.

I think that it may be okay for the Buddhist family to have an event for the couple in which the couple is blessed in a Buddhist ceremony, but this ceremony cannot include the exchange of matrimonial consent between the couple.

It is also not permitted to have a duel ceremony where a Catholic priest and a non-Catholic minister co-officiate. The non-Catholic minister may perhaps say a few words and a blessing at the wedding, but cannot officiate.

All of this is called canonical form and is required in order for your son to marry with the blessing of the Church. It is possible, however, for the Bishop to dispense the requirement for canonical form.

When the time comes for preparation of marriage, your son needs to contact the Diocese to apply for a dispensation (or the parish priest may do this).  It is unlikely the parish priest will know the information about what can or cannot be done with a Buddhist ceremony, so contacting the Marriage Tribunal at the Diocese is probably prudent.

God Bless,
Bro. Ignatius Mary