Whereas early thermal models of honeycomb transparent insulation assumed the honeycomb to be bounded by opaque plates on both faces, more recent models have allowed for an air gap between the honeycomb and one of the plates: the "compound honeycomb" configuration. This paper deals with a new configuration, one that is basically the compound honeycomb configuration, but the other bounding plate is diathermous (i.e., partly transparent to long-wave radiation) rather than opaque. This new configuration has arisen in the application of honeycombs in greenhouses. This paper extends the existing compound honeycomb model, by adding a new variable and a new equation. It was found that a 9 x 9 matrix needs to be inverted rather than the 8 x 8 required by the earlier formalism. To test the model, the overall conductance across a set of transparent honeycombs resting on one of two diathermous plastics was measured, using a guarded heater plate apparatus. The honeycombs were fabricated from UV-stabilized polypropylene, and had a cell size of about 10 mm. Although the model tended to slightly over-predict the measurements (by about 10%) it is considered to be accurate enough for design purposes. (C) 2003 Elsevier Ltd. All rights reserved.