Methods for obtaining estimates of seepage into drifts and tunnels excavated in unsaturated fractured rocks are of interest for engineering and environmental applications. For uniform porous media a tunnel surface may present a capillary barrier promoting water diversion around the opening through the porous matrix, hence reducing seepage into the opening. The presence of fractures intersecting the opening complicates flow behavior and presents a challenge to seepage prediction. We present a simple and physically based model for seepage estimation that preserves key physical processes associated with fracture flow, while avoiding complexity of detailed fracture network characterization. The processes of film and capillary-driven flows are combined with a geometrically tractable representation of the dual-continuum fractured rock with two disparate populations of matrix pores and fracture apertures. The large disparity in capillary forces between matrix and fractures rules out matrix seepage based on Philip's theory. We obtain estimates of seepage fraction for a given percolation flux from consideration of the hydraulic conductivity of the fracture domain only. Similar to previous studies, the new model shows existence of a percolation threshold for onset of seepage. The new model also exhibits a steep increase in seepage with increase in percolation flux that reflects the role of fracture film flow. In addition to consideration of physically based flow processes, computations for the proposed analytical model can be performed with common spreadsheet software, which is a distinct advantage over numerical equivalent porous media approaches that require a powerful computational environment, excessive computation time, and thorough characterization of the fracture domain.