When do you see false triggerings, and where exactly? Have you tried to use a Faraday shield, connected to signal ground?

At which inputs do you have the 100nF caps installed? Take care, if such a cap is fed by an output of micro, this output sees a short circuit, resulting in huge ground bounce! The cable to the keypad and the keypad itself should be shielded. Filters can be used, but must match the keypad reading routine timing affordnesses, means must slew fast enough. You should add some protection circuitry at the keypad lines. Schottky diodes (BAT54S) to the supply rails, for instance.

We should have a look at the PCB. Do you have a solid ground plane? Enough distance to the relays? All inductive loads "free-wheeled" or "snubbered"?

Kai Klaas