This processor's graphics subsystem is capable of simultaneously supporting three DisplayPort (DP) 1.2 output streams and each of these is capable of supporting a 4K@60Hz display. From what you've stated, one of these streams is directly available at a DP connector. In order to support a HDMI connector, the board will include a LSPcon chip which performs the DP-to-HDMI conversion. Whether the chip utilized is capable of supporting HDMI 2.0 (and 4K@60Hz) is dependent upon choice and firmware. You haven't provided a proper part number for your motherboard, so I cannot determine whether this motherboard has the support necessary. Note also that you should be checking your manufacturer's support website for firmware updates for this chip.
Hope this helps,