BAGHDAD -- The next U.S. president will be the fifth in a row with troops fighting in Iraq.

Iraqi forces are encircling the city of Fallujah, a major provincial capital west of Baghdad that was seized by ISIS two years ago. In an unusual alliance -- to say the least -- both the U.S. and Iran are helping.

Families escaped Friday any way they could. Crossing the Euphrates River outweighed the risks of being trapped inside Fallujah as Iraqi forces slowly encircle the city and the ISIS militants that still control it.

Iraqi women and children who fled the violence in their village of Saqlawiyah, north west of Fallujah, wait to receive aid at a military point outside their village, on June 3, 2016. AHMAD AL-RUBAYE/AFP/Getty Images

The assault is being spearheaded by U.S.-trained Iraqi Special Forces. There are also Iranian-backed Shiite militias and even local Sunni tribal fighters taking part, all backed up by airstrikes from the U.S. and its allies.

Yet any hopes of a swift victory have been shattered by ISIS' fierce defense.

Iraqi military officials told CBS News troops have run into unexpectedly heavy resistance. Mortars, snipers and countless roadside bombs have stalled the advance on the southern outskirts of the city.

ISIS fighters have had an iron grip on Fallujah since capturing it two years ago.

Now, as Iraqi forces edge toward the city itself, Iraqi commanders told CBS News the estimated 50,000 civilians who live there make it much harder to call airstrikes in. The battle will likely go street by street and house by house.

The commander of the Iraqi Special Forces also said they also fear that ISIS will use civilians as human shields. He said ISIS fighters have moved from the government buildings they occupied to family homes, where snipers have taken up positions with the residents inside.