Cokecan
The F-15E did fly captive carry tests with the AGM-88 HARM, but the weapon is not carried operationally (it was carried on the outboard wing pylons, which have also never been fitted operationally).
The mixed load AIM-7/AIM-120 combo was fairly typical in OSW/ONW, where "the threat" was not considered to be very capable. The rationale explained to me by F-15E aircrew at the time was that the USAF's AIM-7 stocks were approaching the end of their shelf life. There was a preference therefore to employ the Sparrow before the AMRAAM when conditions allowed, and that meant carrying the mixed load.
In the end it was all academic - there were no air-to-air engagements by the F-15E in either OSW or ONW. Ditto for the C-model Eagle.