Glioblastoma treatment planning commonly relies on the contrast-enhancing tumor volume identified on MRI. Infiltrating tumor cells, however, frequently extend beyond this volume, which impacts outcome. Accurately detecting and segmenting these infiltrative regions is therefore critical for optimizing surgical and radiotherapy planning. Histopathological studies indicate that the [18F]FET PET-positive volume may offer more complete coverage of the tumor and its infiltration, but is not always available. We combine [18F]FET PET labels with conventional MRI labels to enable a more comprehensive segmentation of the glioblastoma tumor volume and investigate whether such segmentation can be achieved using MRI alone. To achieve this, we introduced two novel hybrid tumor definitions: the hybrid tumor core and the hybrid whole tumor, derived from a combination of MRI and [18F]FET PET labels. We subsequently trained a nnU-Net-based segmentation model to predict these labels using combined MRI and PET data and implemented two strategies to handle missing PET data. The hybrid segmentation achieved DSC and NSD of 0.889 and 0.682 for HybTC, and 0.929 and 0.835 for HybWT, respectively, which is on par with separate segmentation. Results demonstrated that while the proposed strategies could partly compensate for the missing PET images, the performance remained significantly lower compared to the segmentation including PET. Since consistently predicting infiltration as defined by [18F]FET PET from MRI alone currently remains unfeasible, the findings support the continued inclusion of PET imaging in glioblastoma management.