Not exactly at eachother's throats.
http://www.cfr.org/publication/11275/Introduction
Experts disagree over the nature of the relationship between al-Qaeda and Hezbollah. Some analysts see the groups as natural allies because of their common interests, while others perceive hostility stemming from sectarian rivalry: Al-Qaeda is a Sunni group and Hezbollah is Shiite. Representatives for the groups have at times spoken unfavorably of one another, though al-Qaeda spokesman Ayman al-Zawahiri bridged the rhetorical divide in a July 27 video in which he acknowledged Hezbollah's fight against Israel is indeed jihad, saying "We cannot just stand idly by while we see all these shells fall on our brothers in Gaza and Lebanon." In fact, evidence suggests al-Qaeda and Hezbollah have cooperated in the past and may do so again.
Do Hezbollah and al-Qaeda work together?
They have in the past. As former National Security Council members Daniel Benjamin and Steven Simon describe in their book, The Age of Sacred Terror, a small group of al-Qaeda members visited Hezbollah training camps in Lebanon in the mid-1990s. Shortly thereafter, according to testimony from Ali Mohammed, an Egyptian-born U.S. Army sergeant who later served as one of bin Laden's lieutenants and pled guilty to participating in the 1998 embassy bombings in eastern Africa, Osama bin Laden and Imad Mugniyeh met in Sudan. The two men, who have both topped the FBI's list of most-wanted terrorists, agreed Hezbollah would provide the fledgling al-Qaeda organization with explosives and training in exchange for money and manpower. Though it is unclear whether all terms of that agreement were met or the degree to which the two groups have worked together since. Douglas Farah, a journalist and consultant with the NEFA Foundation, a New York-based counterterrorism organization, says Hezbollah helped al-Qaeda traffic its assets through Africa in the form of diamonds and gold shortly after the 9/11 attacks. U.S. and European intelligence reports from that time suggest the two groups were collaborating in such activities as money laundering, gun running, and training. It's not clear whether these past collaborations were isolated incidents or indications of a broader relationship.
Do al-Qaeda-Hezbollah ties pose a threat to the United States?
Some experts are increasingly concerned by the threat posed by Hezbollah outside its normal area of operations. "I think we should be quite concerned," Farah says, "Hezbollah will eventually be pushed back a bit and will see striking outside their borders as the way to go." There is already some evidence suggesting the United States could be a target. According to Ed Royce, chairman of the House subcommittee on terrorism and non-proliferation, "We're seeing a pattern of activities on the border and elsewhere," he told UPI, "a renewed operational focus by Hezbollah on getting their people in over the border."
Last month the FBI sent a notice to 18,000 police agencies asking them to remain wary of the Hezbollah threat. This is not the first time the FBI placed Hezbollah in its sights: A 2002 report from the agency suggested that fifty to one hundred Hamas and Hezbollah agents had infiltrated the United States at that time and were involved in fund-raising and low-level intelligence gathering. Just last year, ABC News reports, the Bureau had as many as 200 active cases involving suspected Hezbollah operatives. Hezbollah's intelligence gathering activities have been seen by some officials as contingency planning should either group wish to launch attacks in the United States. The group has consistently shown itself to be one of the most innovative and effective terrorist groups in the world. As then-Deputy Secretary of State Richard Armitage explained in a September 2002 speech, "Hezbollah may be the A team of terrorists and maybe al-Qaeda is actually the B team." Some experts say a Hezbollah attack in the United States isn't very probable. Former FBI counterterrorism agent Jack Cloonan told ABC, "The more likely scenario will be that Hezbollah will target a U.S. facility overseas."