The process of delineating a region of interest or an object in an image is called image segmentation. Efficient medical image segmentation can contribute to the early diagnosis of illnesses, and accordingly, patient survival possibilities can be enhanced. Recently, deep semantic segmentation methods demonstrate state-of-the-art (SOTA) performance. In this paper, we propose a generic novel deep medical segmentation framework, denoted as Ψnet. This model introduces a novel parallel encoder-decoder structure that draws up the power of triple U-Nets. In addition, a multi-stage squeezed-based encoder is employed to raise the network sensitivity to relevant features and suppress the unnecessary ones. Moreover, atrous spatial pyramid pooling (ASPP) is employed in the bottleneck of the network which helps in gathering more effective features during the training process, hence better performance can be achieved in segmentation tasks. We have evaluated the proposed Ψnet on a variety of challengeable segmentation tasks, including colonoscopy, microscopy, and dermoscopy images. The employed datasets include Data Science Bowl (DSB) 2018 challenge as a cell nuclei segmentation from microscopy images, International Skin Imaging Collaboration (ISIC) 2017 and 2018 as skin lesion segmentation from dermoscopy images, Kvasir-SEG, CVC-ClinicDB, ETIS-LaribDB, and CVC-ColonDB as polyp segmentation from colonoscopy images. Despite the variety in the employed datasets, the proposed model, with extensive experiments, demonstrates superior performance to advanced SOTA models, such as U-Net, ResUNet, Recurrent Residual U-Net, ResUNet++, UNet++, BCDU-Net, MultiResUNet, MCGU-Net, FRCU-Net, Attention Deeplabv3p, DDANet, ColonSegNet, and TMD-Unet.