Reliability analysis is used to evaluate the probability of failure of a flood defence embankment subject to a blanket layer foundation condition, where high seepage forces increase the likelihood of internal erosion and slope failure. The stochastic effect of hydraulic conductivity and blanket layer thickness, in addition to soil shear strength properties, is considered for the underseepage and slope stability failure modes using the first-order reliability method. The blanket layer thickness controls the factor of safety (F) and reliability, followed by the unit weight of the blanket layer. Despite variation over orders of magnitude, hydraulic conductivity is less important than and comparable to the effect of soil shear strength parameters. Aleatory uncertainty is evaluated using fragility curves and a confidence interval on the expected value of F (stochastic F). Uncertainty in probability distribution parameters allows quantification of a subset of epistemic uncertainty and is used to construct confidence intervals for fragility.