Dichotomous DV and 3 points of measurement per condition within each subject

I have been reading a lot on this site and I think I am going to analyze my data using a mixed model ANOVA- random effect= subject and 2 fixed effects- comparison and pricing (each have 2 levels). All of my subjects were in all 4 conditions (a cross between the 2 factors) and answered 3 items in each condition. The catch is that my DV is dichotomous. I read that it is not a good idea to assign a mean (i.e. proportion in this case) of the 3 items for each subject and then do the ANOVA using that because my DV is binary. Does this mean that I will have (number of subjects) * 3* 4 observations?