Good morning! Thanks for posting! here is quck breakdown between the chipsets.
H67 has integrated graphics and usualy 1 PCI-E x16 connector for expansion capapbilities.
P67 needs a discrete graphics card, and usually offers 2 PCI-E x16 connectors for multi-card configurations
Z68 is basically the same as P67 but offers QucikSync for transcoding, but barely anyone uses this because very few apps support it.
So in short yes, your H67 can and will be able to run GTX560.
You will Need a 500W power supply or higher that accomadates 2 PCI-e 6 Pin Power Connectors. I would suggest a 600W power supply.
Here is the power supply I have, and am currently running a Gigabye GTX680 on it which is way more beefier than the 560 Ti.
Here is your Nvidia Spec Sheet on the GTX 560 Ti
If this answered your question please mark it as so! If not, reply, and I'll keep helping!