Is R-38 between joists plus R-15 continuous insulation enough for a flat roof in DC?

Short answer. Yes — and the R-15 exterior board is not an arbitrary number. It is the exact minimum the code sets for condensation control on an unvented low-slope roof in DC's climate. Washington DC is ASHRAE Climate Zone 4A (mixed-humid). Two separate checks decide whether a flat-roof assembly is sound: the energy R-value minimum, and — the one that actually governs a flat roof — condensation control.

1. Energy R-value (2015 IECC): comfortably met

The assembly's nominal total is about R-53 (R-38 in the joist cavity plus R-15 continuous).

• Residential path (Table R402.1.2, Zone 4): the ceiling requirement is R-49. The exception that lets R-38 substitute for R-49 is attic-only — it requires the full-height R-38 to extend over the wall top plate at the eaves — so a between-joist flat roof cannot use it. But R-38 + R-15 continuous = R-53, which exceeds R-49 on its own, and the continuous layer removes framing thermal bridging so the U-factor is better still.
• Commercial path (Table C402.1.3, Zone 4): insulation entirely above deck = R-30 c.i.; attic-and-other = R-38. The R-38 cavity meets the attic-and-other value by itself, and the R-15 continuous is on top of that.

Either way, the assembly exceeds DC's energy minimum.

2. Condensation control — the item that governs a flat roof

A flat or low-slope roof is almost always an unvented compact assembly, so it falls under IRC R806.5. Table R806.5 sets the minimum rigid-board or air-impermeable insulation R-value directly above (or below) the roof sheathing, by climate zone:

The R-15 exterior board equals the Zone 4A minimum exactly. The exterior layer's job is to keep the underside of the sheathing above the dew point, so no condensation forms there.

Why a flat roof is built unvented, not vented

It is tempting to think "to stay dry, vent it." That is true for a pitched roof, where the soffit-to-ridge height difference and the slope drive real airflow. A flat roof has no such height difference — a "vented" flat cavity is stagnant, a way in for moisture with no drying airflow out. Worse, in a mixed-humid climate the outdoor air drawn in during summer is warm and humid; it meets the deck underside (cooled by the air conditioning below) and condenses inside the assembly. Venting a flat roof can add moisture rather than remove it. So the strategy inverts: instead of flushing moisture out with air, you prevent condensation (exterior insulation keeps the deck warm), air-seal so moist air cannot get in, and let the assembly dry slowly to the inside.

Why you must not add an interior vapor barrier

The exterior roofing membrane (EPDM, TPO, or modified bitumen) is already a vapor barrier, and an assembly should have only one. An unvented roof cannot dry outward, so it must be able to dry inward. Adding an interior foil or poly vapor barrier on the ceiling side would create a double vapor barrier that traps any moisture that gets in. R806.5 prohibits interior Class I vapor retarders on the ceiling side of an unvented assembly for exactly this reason.

Watch-items

• R-15 is the minimum, with no margin. If the design increases the cavity insulation without increasing the exterior layer, the condensing plane moves inward — recheck it. More exterior continuous insulation is always safer; for margin, use R-20.
• Seal the rigid board at each sheet's perimeter to form a continuous layer.
• Keep it genuinely unvented — no accidental vented gap that bypasses the exterior insulation.
• No interior Class I vapor retarder on the ceiling side.

Building code determinations are jurisdiction- and edition-specific; confirm the adopted code in force for your project.