If your ticket originates or terminates in the USA, the baggage allowance for the marketing carrier of the first segment applies to all remaining segments. For purposes of this response, we're going to presume its a USA ticket at one end or the other.

If you purchase a single ticket and the two (or more) carriers have an interline baggage agreement (likely unless your domestic is on WN or somesuch):

A-B Carrier #1 (domestic)
B-C Carrier #2 (nternational)
C-B Carrier #2 (international)
B-A Carrier #1 (domestic)

Your baggage allowance for B-C-B-A will be whatever Carrier #1 (presuming that it is not only the operating, but marketing carrier) provides for a baggage allowance (stripped of waivers for elite status and the like).

If your two (or more) carriers do not have an interline agreement or your connection is too long (overnight in most cases), you will have to collect your bags and pay anew if your allowance does not cover whatever it is that you are checking.

If your ticket does not touch the USA, ignore this post !