We present the results of multifrequency observations of two asymmetric, Mpc-scale radio sources with the Giant Metrewave Radio Telescope (GMRT) and the Very Large Array (VLA). The radio luminosity of these two sources, J1211+743 and J1918+742, are in the Fanaroff-Riley class II (FRII) range, but have diffuse radio components on one side of the galaxy while the opposite component appears edge-brightened with a prominent hot-spot. Although the absence of a hot-spot is reminiscent of FRI radio galaxies, suggesting a hybrid morphology, the radio jet facing the diffuse lobe in J1211+743 is similar to those in FRII radio sources, and it is important to consider these aspects as well while classifying these sources in the FR scheme. The observed asymmetries in these Mpc-scale sources are likely to be largely intrinsic rather than being due to the effects of orientation and relativistic motion. The formation of a diffuse lobe facing the radio jet in J1211+743 is possibly due to the jet being highly dissipative. The low-frequency spectral indices of the lobes are in the range of approximately -0.8 to -1, while at the outer edges these vary from approximately -0.65 to -1.05 suggesting steep injection spectral indices, which need to be examined further from observations at even lower frequencies by telescopes such as the LOw Frequency ARray (LOFAR).