While saying Shnayim Mikrah V'echad Targum, it is best not to talk. Magen Avraham (285:11) writes:
וְטוֹב שֶׁלֹּא יַפְסִיק כְּלַל בְּשִׂיחָה
It is good to not interrupt at all by speaking.
Ba'er Heiteiv (285:1) goes even further:
ואיסור גדול להפסיק בקריאת שמו״ת בדיבור
And it is a great prohibition to interrupt while reading Shnayim Mikrah V'echad Targum with speech.
What about a week when we read a double Sidrah? May one speak between the two Sidrahs?