Exposures in bernoulli glm()

Hi, is it possible to add exposures to a glm with family=binomial()?

It's easy to do it for a Poisson/negative binomial: just multiply the 
mean by the exposure, that is, offset(log(exposure)): but this obviously 
wrong for a binomial/Bernoulli since the mean must be no bigger than 1.

My goal was do it it with pscl::zeroinfl and pscl::hurdle, but answering 
for binomial/Bernoulli would already help.