Your Adobe XD project, when using desktop preview, has the ability to show one artboard as an overlay (or pop up) over another artboard. You can mostly do the same thing in the exported page.
To show an overlay you would start following the same steps in Adobe XD prototyping.
Select the artboard and switch to prototype mode. Find an element and add an interaction to add an overlay.
Position the overlay where you desire.
Select the overlay (the artboard) and add a Go Back interaction.
Open the layers panel and select all the overlays. Drag them to the top of the layers list.
Now, select the overlays and then the artboards and then open the Export Artboards dialog.
Choose the Selected Artboards option. Choose the Single Page Application.
Now all the selected artboards and the overlays will be on the page.