The Mishna Berura in 285:6 says that if it is possible for one to not interrupt shnayim mikrah viechad targum for any matter, it is a very good thing. The Shaar Hatzion (11) says it appears that this true even between two parshiyos. However, he says that it is assur min hadin to interrupt if one is in the middle of an “inyan”. Firstly, what is considered an “inyan” for the purposes of this halacha. Secondly, how far does this prohibition of interrupting go. For instance, if one is doing shnayim mikrah and is in the middle of an “inyan” and he is greeted by another person or asked a question by another person, should he not respond to them?
An inyan would be between what the Shar Hatzion says is between parsha l’parsha, meaning at a “peh” or “samach”, which are a sign that there is a space between parshios. Regarding talking out in middle of a parsha, it is permitted to answer a davar shebikidusha, such as amen, kidusha, borchu, and kaddish. If one needs the bathroom he may say Asher yotzar afterwards, And according to some poskim if he needs a drink he may say a bracha on it. R’ Y. Belski zt”l held that talking in learning is permitted, however idle talk is not allowed during being maavir sedra.
Kaf Hachaim 15, Halichos Shlomo Tefillah 12:ftnt. 105, Divrei Chachumim page 93.