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Three-phase suspensions, of liquid that suspends dispersed solid particles and gas bubbles, are common in both natural and industrial settings. Their rheology is poorly constrained, particularly for high total suspended fractions (≳0.5). We use a dam-break consistometer to characterize the rheology of suspensions of (Newtonian) corn syrup, plastic particles and CO 2 bubbles. The study is motivated by a desire to understand the rheology of magma and lava. Our experiments are scaled to the volcanic system: they are conducted in the non-Brownian, non-inertial regime; bubble capillary number is varied across unity; and bubble and particle fractions are 0 ≤  ϕ gas  ≤ 0.82 and 0 ≤  ϕ solid  ≤ 0.37, respectively. We measure flow-front velocity and invert for a Herschel–Bulkley rheology model as a function of ϕ gas , ϕ solid , and the capillary number. We find a stronger increase in relative viscosity with increasing ϕ gas in the low to intermediate capillary number regime than predicted by existing theory, and find both shear-thinning and shear-thickening effects, depending on the capillary number. We apply our model to the existing community code for lava flow emplacement, PyFLOWGO, and predict increased viscosity and decreased velocity compared with current rheological models, suggesting existing models may not adequately account for the role of bubbles in stiffening lavas.