If you want to keep the two things separate, make sure they are components or groups. In your example, it appears that both things are identical. You could just copy the bottom one up by the thickness of the thing plus the 10mm. Use Move/Copy for that.

Have you learnt about groups and components yet? By grouping geometry you stop it sticking to loose geometry. therefore allowing you to move it around freely as an object. A chair for example that isn't part of the floor it sits on. A component is a group that is easily repeatable. So your chair may have four legs that are made from one component, change one leg and you change all four, and they don't stick to other geometry. So to answer your question, if you have a chair, select all of it and make it a component. Then in the edit menu select copy, then paste or paste in place. Paste will give you a chair on your cursor until you click to place it, and paste in place will paste it on top of the original, but it will be a separate thing that can be selected and moved. The move tool allows you to copy in one step. With your chair selected use the move tool and crtl to create and place a copy or an array.

Thanks