Appalachian Communities Health Emergency Act or the ACHE Act This bill requires the National Institute of Environmental Health Sciences to conduct or support studies on the health impacts of mountaintop-removal coal mining on individuals in the surrounding communities. The Department of Health and Human Services (HHS), upon receiving the results of these studies, must determine whether such mining presents any health risks to individuals in those communities. The bill applies to surface coal mining that uses blasting with explosives in the steep slope regions of Kentucky, Tennessee, West Virginia, and Virginia. The bill prohibits specified agencies from issuing permits for any mountaintop-removal coal mining project or expansion unless HHS determines that such mining does not present any health risk to individuals in the surrounding communities. The bill requires monitoring of air, water, and soil for pollution, including noise pollution, until HHS makes its determination. HHS must publish pollution-monitoring results. The Office of Surface Mining Reclamation and Enforcement of the Department of the Interior must assess a one-time fee upon existing mining projects, sufficient to cover the federal cost of the studies and pollution monitoring required by the bill.