The bug

After re-loading (and getting the Mojang Studios loading screen), the Minecraft music stops for 5 minutes or so until it plays again. This also happens with jukeboxes.

What I expected to happen (with the Minecraft music)

I expected it to pause the Minecraft music and then continue playing after it's reloaded.

What I expected to happen (with the jukebox)

If it's on singleplayer, I would expect it to pause and then resume the music disc.

If it's on multiplayer (or a LAN world), then I would expect it to not pause the music disc, but instead just to resume it where it's at server-side.

How to replicate (with normal background Minecraft music)

1. Wait until Minecraft plays a default song (for example C418 - Wet Hands).
2. Reload your resource packs (F3 + T), or get Minecraft to go to the Mojang Studios loading screen. 

How to replicate (with jukeboxes)

1. Play a disc in a jukebox (for example, Pigstep).
2. Reload your resource packs (F3 + T), or get Minecraft to go to the Mojang Studios loading screen. 

Note

Does it work even without mods and with the original launcher?
Yes.