This article examines the choices of Polish households in their decision to consume and the amount spent on four dairy products, i.e., whole milk, skim milk, butter and yogurt. A random utility framework leads to the specification of a system of four participation and four level (expenditure) equations. With the strong substitution effect between the consumption of whole milk and low-fat milk and possible correlation among the purchase decisions of other dairy products, the specification allows for correlation between the consumption decisions among different dairy products. Therefore, the selection of a system approach leads to constructing a multivariate two-part model. A pooled cross-sectional sample used in model estimation has 77,043 observations with non-missing values for the period from 2005 to 2008.