We broke the story ... Anna gave birth to the twins, a boy and a girl, and while she was secretly pregnant, the couple started building a huge 16-foot-tall wall around their Miami home. Construction started in late summer, deep into Anna's 2nd trimester.

According to city building permits, they're also adding a 2-story single family residence to their property -- along with baby-proofing measures, like a "child barrier for pools."

The wall makes sense. Privacy is totally Enrique and Anna's M.O. -- since they clearly went though a whole pregnancy without anyone ever knowing.

The docs say the home makeover will cost $600k when it's all said and done.