[JRTJH]

You can't run both hot and cold water through the same filter. If you do, you'll have two inputs (H & C), "Tee'd" to one input at the filter inlet and only one output to the faucet. You won't be able to control the water temperature because both faucets would have to be connected to the "single output" from the filter.

If you want to filter both the hot and cold with one filter, you'd have to do it either just after the pump (with a single filter) located before the supply splits to hot/cold, or you'd have to have two filters, one for the hot supply and one for the cold supply located just before the water enters the faucet.