I am doing a difference-in-difference analysis on a set of survey data for a health education program and I need to find statistical significance for the difference-in-difference estimate. I know that I find this using a regression. I need to use a regression in a mixed logistic model including pre/post intervention, treatment group (intervention/control), gender, age, school, and classes in each school as covariates (6 variables). The issue is that I am not sure how to write the regression equation for all these variables.

I have only seen examples where a difference-in-difference estimate is made with a regression of two variables and their interaction term, like the following equation:
Y=α+β1Treat+β2Post+β3(Treat ⋅ Post) +ϵ
β3 will be the difference-in-difference estimate for this regression and will give the p-values for the difference-in-difference estimate.

How do I write the regression equation with all six variables? Which constant will be the difference-in-difference estimate in that equation?
Resources or explanations on how to do this would be much appreciated. If you just know the answer to the first question I would appreciate that too.