Are there rim brakes for road bikes compatible to Shimano hydraulic brake levers / brifters? Are there any rim brake calipers with road-style mounting compatible to Shimano hydraulic brake levers, specifically ST-U5060? 


are Magura ST-06 / ST-08 compatible?people combine Magura disc callipers with shimano levers succesfully, dubbed "shigura", but I couldn't find a hint of anyone having combined ST-06/08 with any other lever. I guess they're too uncommon for this.


I'm looking for a way to have both shift- and brake levers on a triathlon bar's horns, like this question or this question. To my knowledge, there's only:


the ST-U5060 that's only for hydraulic disc brakes
a combination of brake levers clamping on the horn outside and SRAM shifters 
-I couldn't find the brake levers. 
drop bar brifters on the horns (which results in an awkward angle of the levers on my particular triathlon bar)
I would pick up a pair of cyclocross-style brakes levers that are designed to mount on the flat part of the bar and run inline with the brake cables. You can also mount them to the end of the bar and just have the cable terminate at the lever. The angle might not be quite right with the bullhorns, but some levers come with an adjustment screw that lets you set the default position of the lever. I would make sure to get some like that. And then you can just use whatever bar-end shifters you want.