I think this is not a problem of using model in torchvision. What you want seems like to use the model to output binary vector, instead of the original output you get from the model directly.
Firstly, you need to have your own method of getting 0 or 1 based on the output of the model, like if the model output [-2.3, 4.4, 2.0, -0.8], you need to specify what binary it should output. Like for conventional softmax method for single-label task, they select the maximum to be 1 and all others 0.
Then, you have your output of the original model, which is not binary, and the target binary value, and (maybe?) you can extend the definition of cross entropy to multi-label task (where the target is not a single 1 binary vector).
Hope this helps.