Intel socket LGA1150 CPUs have an embedded memory controller, meaning that it is the processor, not the chipset, that defines what memory technologies you can have and the maximum amount of memory that is possible. The motherboard, however, may have a limitation as to how much memory can be installed.
The integrated memory controller from socket LGA1150 processors supports DDR3 memories up to 1,600 MHz. According to Gigabyte, the H81M-S2PH also supports memories up to 1,600 MHz.
The Gigabyte H81M-S2PH has two memory sockets. Since DDR3 memory modules can be found in capacities up to 8 GiB, you can have up to 16 GiB with this motherboard if you use two 8 GiB modules.
In order to enable the dual-channel mode, you must install two identical memory modules.