When lists are unboxed, TeX does not re-calculate baseline-to-baseline spacing, the contents of the boxes are simply added directly to the current list.
So (when feasible) it is simplest to arrange that the list being unboxed have the correct spacing. In this case the main controlling parameter is \prevdepth
, if you force the paragraph to end before ending the first box, you can save \prevdepth
and then set \prevdepth
at the start of the second box to force the correct baselineskip calculation for the first line,

\documentclass{report}
\usepackage{lipsum}
\setlength\parindent{0pt}
\linespread{2}
\begin{document}
\setbox0=\vbox{\lipsum[1]\par\global\dimen1=\prevdepth}
\setbox2=\vbox{\prevdepth=\dimen1 \lipsum[2]}
\unvbox0
\unvbox2
\end{document}
\addvspace{\baselineskip}