Boolean Difference/Boolean Union Issue

I have an issue with Boolean dirrefence and boolean union. They work as opposites, meaning BU ( B. Union) cuts out my surfaces and B. D ( B. Difference) joins them. I have no idea how to fix this. Please help!!!

Hi Antonia - see Boolean Frequently Asked Questions [McNeel Wiki]

Scroll down to the bit about Booleans and open objects. (But read the whole thing anyway)