Apple giveth Apple Music, and Apple taketh away. In this case, the MIA feature is Home Sharing for music files to your iPhone, iPad or iPod Touch.
The iOS 8.4 update brought with it Apple's Beats-powered music subscription service, Apple Music, but along the way, Apple has rather quietly killed the ability to stream music from a nearby computer running iTunes to your iOS 8.4 devices. Home Sharing allowed for both music and video sharing to your portable devices, but as of iOS 8.5, it's been limited to video only.
Home sharing of music is still feasible to Apple TV, but not other devices. It's feasible, based on release notes for the iOS 8.4 betas that state that home sharing was "not currently available" that this is just a bug that Apple accepted for the initial 8.4 release. Or that Apple really wants you to switch to streaming via Apple Music only.