Miriam's husband was Caleb son of Yefuneh of the tribe of Judah.
Caleb was one of the twelve spies sent to reconnoiter the Land of Canaan, in preparation for the Israelites' impending invasion of Israel. He and Joshua were the only two scouts who did not go along with the negative and pessimistic report provided by the other ten scouts. Instead they encouraged the people to have faith in G‑d's ability to deliver Canaan's inhabitants into their hands. Caleb famously told the Jews: "Didn't Moses split the sea, bring down the manna, and cause the quails to fly down to us? We can surely go up!... We will succeed in whatever Moses says!"
Caleb's role is even more remarkable than Joshua's. Before embarking on their mission, Moses prayed on behalf of his trusted assistant Joshua, which explains why he didn't succumb to the scouts' nefarious plot. Caleb, however, was "on his own." As soon as he reached Canaan he headed for the Cave of Machpelah where the Patriarchs and Matriarchs are interred, and pleaded with them to intercede with G‑d to give him the necessary courage and strength to remain faithful to his mission.
Obviously, Caleb was a man of great caliber. His upright character and actions in the incident with the spies is discussed at great length in the Torah (Numbers 13-14).
In the aftermath of the spy debacle, G‑d decreed that all the adult, male Israelites would perish before the nation entered the Promised Land. Only Joshua and Caleb were given immunity from this decree, due to their courage and faith.
And they were both handsomely rewarded. Joshua succeeded Moses as the next Jewish leader, and Caleb was given the city of Hebron as his personal inheritance -- not incidentally, the city which houses the Cave of Machpelah.
Miriam and Caleb were two courageous leaders who were eminently suited for each other. Miriam "earned her stripes" in Egypt, when as a Jewish midwife she stood up to Pharaoh's demand that she murder Jewish babies.
According to Jewish tradition, Caleb was also one of the two scouts sent by Joshua to Jericho immediately before the Jews crossed the Jordan River and entered Canaan.
Chana Weisberg for Chabad.org