Composite acoustic panels are provided which may usefully be employed for aircraft interior panel assemblies. The composite acoustic panels may include a core member defining opposed surfaces, and a pair of exterior face sheets each attached to a respective one of the opposed surfaces of the core member. At least one of the face sheets may be microperforated. The core member comprises an adjacent plurality of tubular channels extending through a thickness dimension of the core member between the opposed surfaces thereof, while predetermined adjacent ones of the tubular channels are filled with a material to define a series of filled tubular channels which are adjacent to a region of open tubular channels. Certain ones of the open tubular channels may be partially filled with an acoustic dampening material. Discontinuous viscoelastic layers may be positioned so as to overlay central regions of the adjacent plurality of the open tubular channels which are bounded by an array of the filled tubular channels.