Aims. The FR I/FR II dichotomy is a much debated issue in the astrophysics of extragalactic radio sources. Study of the properties of HYbrid MOrphology Radio Sources (HYMORS) may bring crucial information and lead to a step forward in understanding the origin of FR I/FR II dichotomy. HYMORS are a rare class of double-lobed radio sources where each of the two lobes clearly exhibits a different FR morphology. This article describes follow-up high resolution VLBA observations of the five discovered by us HYMORS. The main aim of the observations was to answer the questions of whether the unusual radio morphology is connected to the orientation of objects towards the observer. Methods. The milliarcsecond-scale structures are good probes of the galactic medium, the possible asymmetries, and orientation of the central engines of the sources. We obtained the high resolution radio maps of five hybrid radio morphology objects with the VLBA at C-band and L-band. Results. The cores of all five sources have been detected at both radio bands. Two of them revealed milliarcsecond core-jet structures, the next two objects showed hints of parsec-scale jets, and the last one remained point-like at both frequencies. Conclusions. We compared properties of observed milliarcsecond structures of hybrid sources with the larger scale ones previously detected with the VLA. We find that on both scales the fluxes of their central components are similar, which may indicate the lack of additional emission in the proximity of the nucleus. This suggests that jets present on the ~1−10 kpc scale in those objects are FR II-like. When possible, the detected core-jet structures were used for estimating the core’s spatial orientation. The result is that neither the FR I-like nor the FR II-like side is preferred, which may suggest that no specific spatial orientation of HYMORS is required to explain their radio morphology. Their estimated viewing angles indicate they are unbeamed objects. The 178/151 MHz luminosity of observed HYMORS exceed the traditional FR I/FR II break luminosity, indicating they have radio powers similar to FR IIs.