Rules 5.05(b)(3), 5.06(b)(3)(D), 6.01(g):
Under Official Baseball Rule 5.05(b)(3), if catcher’s interference is called with a play in progress, the umpire will allow the play to continue because the manager may elect to take the play—unless the batter reaches first base and all other runners advance one base, in which event the play stands and the manager has no option to take the interference penalty.
The umpire should indicate catcher’s interference by pointing at and calling
The manager shall make the election to take the play or take the interference penalty by advising the plate umpire immediately following the play, and once made, such election cannot be changed.
If the batter-runner misses first base, or a runner misses his next base, he shall be considered as having reached the next base, as referred to in the Note to Official Baseball Rule 5.06(b)(3)(D) and as stated in the Approved Ruling of Official Baseball Rule 6.02(a):
A runner who misses the first base to which he is advancing and who is called out on appeal shall be considered as having advanced one base for the purpose of this rule.
If a runner is attempting to steal a base when the catcher interferes with the batter, the runner is awarded the base on the interference. Runners not attempting to steal or not forced to advance remain on the base they occupied at the time of the interference unless Official Baseball Rule 6.01(g) applies. Under Official Baseball Rule 6.01(g), if a runner is stealing home when the catcher interferes with the batter, the additional penalty of a balk is invoked, which enables all runners on base to advance (whether or not they were stealing).
See also Official Baseball Rules 5.05(b)(3), 5.06(b)(3)(D), and 6.01(g).