New robust stability margins are introduced for continuous-time Markov jump linear systems (MJLS) with uncertain transition rates. A distinguishing feature of our approach is that, through a spectral characterization of stability, we show how the proposed robustness margins are amenable to a linear time-invariant (LTI) description, whereby classical disturbance attenuation techniques can be employed. Our approach aims at ensuring robustness with respect to transition rate uncertainties satisfying a prespecified spectral norm bound, a setup which has not been fully developed in the literature. The robustness margins that constitute our main results are characterized by linear matrix inequalities, and therefore can be efficiently maximized via convex optimization. Driven further by the rationale of bringing classical LTI methods to the robustness analysis of MJLS, we also propose a robustness margin via structured singular values (μ-analysis). Some numerical examples illustrate how our results can outperform some of the existing approaches.