Is it permissible to interrupt one’s recitation of Birkat Hamazon, such as to respond to Kaddish, Kedusha or Barechu?
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Hukat (3; listen to audio recording for precise citation), rules that Birkat Hamazon has the same status as the Amida prayer with regard to interruptions. This means that it is forbidden to interrupt one’s recitation of Birkat Hamazon, even to respond to Kaddish, Kedusha or Barechu. If a person hears Kaddish, Kedusha or Barechu while reciting Birkat Hamazon, he should remain silent and listen, but not verbally respond – just as one should do if this happens as he prays the Amida. Like during the Amida, one may not make any interruptions at all during the recitation of Birkat Hamazon.
The Ben Ish Hai adds that this comparison to the Amida applies also to making gestures or motions. Just as one may not signal or motion to another person during the Amida, this is similarly forbidden during Birkat Hamazon. Unfortunately, many people are not aware of this Halacha. It is forbidden during Birkat Hamazon to make even simple gestures; one must do nothing throughout Birkat Hamazon except recite the text with Kavana (concentration). Thus, for example, one may not snap to get somebody’s attention or make any other motion. In fact, the Ben Ish Hai writes that one may not use a handheld fan to fan himself during Birkat Hamazon. Even a simple activity such as this would be forbidden during Birkat Hamazon.
The exception to this rule is the section of the "Harahaman" prayers which we customarily add after Birkat Hamazon. These prayers are not part of the original Birkat Hamazon, and are recited only as a custom, rather than as part of the strict obligation of Birkat Hamazon. It goes without saying that one should recite the entire section of the "Harahaman" prayers, without making any interruptions. However, since this section is not, strictly speaking, part of Birkat Hamazon, one may – and in fact must – interrupt this section to respond to Kaddish, Kedusha or Barechu, or to answer "Amen" to a Beracha. Furthermore, if some need arises that demands one’s attention, he may briefly interrupt during this section, such as to say, "Just one second" and the like.
Incidentally, if a person hears somebody else reciting the "Harahaman" prayers after Birkat Hamazon, he should answer "Amen" to each "Harahaman." Furthermore, if a person ate with gentiles and recites Birkat Hamazon in their presence, he should change the prayer "Harahaman Hu Yebarech Kol Ehad Ve’ehad Mimenu" ("The Merciful One shall bless each and every one of us") to ""Harahaman Hu Yebarech Kol Ehad Ve’ehad Mi’Bneh Berit" ("The Merciful One shall bless each and every member of the covenant"). Since this prayer was composed as a prayer specifically for Am Yisrael, it must be revised when non-Jews are present.
Summary: It is forbidden to make any interruptions during Birkat Hamazon – even to respond to Kaddish, Kedusha or Barechu. One may not even gesture or motion to somebody, such as by snapping, during Birkat Hamazon. However, during the "Harahaman" section, one should interrupt to answer "Amen" to a Beracha or respond to Kaddish, Kedusha or Barechu, and in situations of needs one may briefly interrupt and then resume the prayer.