We present a seabed profile estimation and following method for close proximity inspection of 3D underwater structures using autonomous underwater vehicles (AUVs). The presented method is used to determine a path allowing the AUV to pass its sensors over all points of the target structure, which is known as coverage path planning. Our profile following method goes beyond traditional seabed following at a safe altitude and exploits hovering capabilities of recent AUV developments. A range sonar is used to incrementally construct a local probabilistic map representation of the environment and estimates of the local profile are obtained via linear regression. Two behavior-based controllers use these estimates to perform horizontal and vertical profile following. We build upon these tools to address coverage path planning for 3D underwater structures using a (potentially inaccurate) prior map and following cross-section profiles of the target structure. The feasibility of the proposed method is demonstrated using the GIRONA 500 AUV both in simulation using synthetic and real-world bathymetric data and in pool trials