Hezbollah said six of its fighters were killed in Lebanon and six in Syria on Monday.
The Iran-backed militia confirmed the death of both fighters.
Hezbollah and the Israeli military have been exchanging fire along the Israel-Lebanon border.
The woman and her children were killed in the village of Sawaneh, the rescue teams said.
Since Hamas militants launched an onslaught in Israel on October 7, more than 4,000 people have died on all sides of the conflict.
Following repeated attacks by the pro-Iranian Hezbollah militia from southern Lebanon, Israel has ordered the evacuation of settlements.
