What is the structure of iodide of Millon's base?
First, ignore any monomeric formula. The compound is definitely polymeric.

The literature contains hints for existence of two separate lines of compounds. The first one is salts of polyamidomercury: $\ce{[Hg(NH2)]_{n}A_{n}}${1} with mercury-amide chains in the structure, and $\ce{(Hg2N)_{n}A_{n}}$ with structure based on crystoballite {2}{3}

It seems thatn the lines are not distinguished in earlier literature, but recent researchers use the words "Millon's base salts" for $\ce{(Hg2N)_{n}A_{n}}$ only.