The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his work Od Yosef Hai (Parashat Shofetim, 50), discusses the severity of the prohibition against relations with a gentile woman (listen to audio recording for precise citation). The punishment for this offense, he writes, is spelled out by the prophet Malachi (2:11), who describes a relationship with a gentile woman with the phrase, "Ba’al Bat El Nechar" (literally, "relations with a foreign goddess"). This description indicates that such relations are deemed equivalent to worshipping an idol. One who engages in relations with a non-Jewish woman – either in the context of marriage, or in a non-marital context – is considered as having desecrated God’s Name, and is liable to the punishment of Karet (eternal excision from the Jewish people). If a person has relations with a non-Jew and she conceives, the child is not considered his child, and is rather considered a gentile, the child of the non-Jewish woman.
The Ben Ish Hai then discusses the prohibitions that take effect the moment a man performs Kiddushin (betrothal) with a Jewish woman. As soon as Kiddushin takes place, when the groom gives the bride a coin or ring, six family members of the bride become forbidden for him, forever, even if the wife dies or the couple divorces. These forbidden relatives are the bride’s mother, maternal grandmother, paternal grandmother, daughter (from a previous relationship), daughter’s daughter, and son’s daughter. If, during times of the Bet Hamikdash, a man engaged in relations with one of these women during his wife’s lifetime, he and the woman would both be liable to the capital punishment of Serefa (burning). If this occurs after the wife’s death, the offenders are subject to the punishment of Karet.
There is also a seventh family member who becomes forbidden to the groom at the time of betrothal – the bride’s sister. Regardless of whether she is the bride’s half-sister or full sister, and whether they share the same father or mother, relations between her and the husband are forbidden. This applies even if the wife’s sister was the product of an illicit relationship between the wife’s father and another woman. However, the wife’s sister differs from the family members listed above in that the husband may marry her after the wife’s passing.
If a man engaged in an adulterous relationship with one of his wife’s aforementioned seven family members – even with full intention to violate the Torah’s sexual code – he may nevertheless remain married to his wife. The only exception to this rule is a case of a groom who engaged in relations with his bride’s sister after Kiddushin, but before the consummation of the marriage. In such a case, he must divorce his wife with a Get; they may not consummate the marriage in this situation.
Summary: It is strictly forbidden for a man to engage in intimate relations with a non-Jewish woman, and this transgression is deemed equivalent to idolatry. The product of such a relationship is considered a non-Jew. When a man betroths a woman, it becomes forbidden for him to engage in relations with her mother and with both her grandmothers, and if she has a daughter from a previous relationship, he may not engage in relations with her daughters or granddaughters. These prohibitions apply even after his wife’s death. A man may, however, marry his wife’s sister after the wife’s death.
