I am not quite sure what you are trying to do, but if it helps, you can control the integra from the JP by selecting the external page in the JP's Registration menu, you will then see the external control option where you can theoretically control all 16 parts of the Integra, by setting up zones and programme / bank changes to each part. This may become a little complicated though.
An alternative would be to set up zones on the integra, with the sounds you want, whereby the split points would match those you select on the Jupiter and save as a studio set on the Integra. Correspondingly, you would save the Jupiters settings as a Registration which could be seen as its equivalent to a studio set. Next you would set a programme change message in the JP to change only the studio set on the Integra, say on channel 16.
I hope this helps. I control a V synth XT from my JP and although it's not a multitimbral, set up the external control facilities on the JP are more than adequate.