How much snow can cover a runway while still allowing commercial airliners to land safely?
There is no set legal limit (ultimately it is up to the PIC to decide) but condition reports are available to pilots at many airports to assist in assessing takeoff and landing performance.   The FAA has recently created a standardized way of reporting runway conditions through their TALPA (takeoff and landing performance assessment) initiative.

TALPA is an improved way of assessing runway conditions, based on contaminant type
and depth, which provides an aircraft operator effective means to anticipate airplane
braking performance. 

The RCAM (shown below) is the tool airport operators use to report a runway surface assessment when contaminants such as water, ice, snow, slush, and others are present on runways, taxiways, and aprons.   To find an updated RCAM look in Chapter 5 of Advisory Circular 150/5200-30, Airport Field
Condition Assessments and Winter Operation Safety.

The RwyCC is the runway condition code -- as you can see a code of 0 yields minimal to non-existant braking and/or directional control.