Camp Half-Blood and Camp Jupiter weren't entirely the most compatible places for the past few centuries due to the higher ups of Camp Jupiter cursing Camp Half-Blood and claiming they would not exchange acts of kindness for ten centuries.
However, this was the year that declared the end of those ten centuries. So with new, but still vicious, leaders of Camp Jupiter came with new rules. A program between Camp Half-Blood and Camp Jupiter was set in place where loyal campers could apply for a trial with the other camp.
A few selected amounts of campers from each camp would attend the opposite site for a week. It was a trial of compatibility between the two, if this went well then it would lead to further collaborations and more opportunities to befriend others of the other camp.
Following the ancient rules, Romans went to the Greeks first. So a few select campers of Jupiter would be attending camp Half-Blood for a week.
It was a bit risky, considering the juxtaposition of teaching styles. The Greeks always had a laid-back atmosphere and focused on individual heroics, while Camp Jupiter, the Roman camp, emphasized order, discipline, and teamwork but it's just an experiment for a reason.