This Reuters report describes clashes with Islamist miltants as part of attacks to retake territory as U.S. backed. It would seem that U.S. special forces are involved in directing Yemeni forces. Perhaps intelligence is provided through drones and perhaps too some of the air attacks are by the U.S. as well. Very often descriptions will be of Yemeni air attacks when they are in fact by the U.S.
Indeed the first strikes by the U.S. in Yemen were all attributed to Yemen until photographic evidence was provided that showed unquestionably that some of the weapons were only in the U.S. arsenal. The reporter responsible for this revelation is still in a Yemeni jail at the request of the U.S. even though Yemen was about to free him!
The territory that the Yemeni government is trying to regain was taken over by Islamic militants last year while protesters including some of the opposition now sharing power were trying to depose former President Saleh. The offensive is causing a humanitarian disaster but that is just collateral damage to increasing the power of the Hadi central government supported by the GCC including Saudi Arabia, and the U.S. See this article for description of the complete humanitarian mess in Yemen.
There has been a pledge of 4 billion in aid to Yemen last month by the Gulf States and western countries but it remains to be seen how much will be delivered and get through to the people who actually need it immediately.
Over 40 per cent of Yemenis live on less than 2 dollar U.S. a day. In May aid agencies said that less than half of Yemenis have enough to eat. Not surprisingly they find nourishment in radical Islamist ideologies. For more see this article.