I have a nephrostomy tube, and for the past few weeks, have been passing urine both through the tube as well as the urethra regularly. is this normal.

Yes: It depends on why the neprostomy tube is there but remember your other kidney is still producing urine out the bladder and urethra.

Can be: Usually a nephrostomy tube is inserted because there is a blockage to the ureter (the tube connecting your kidney to your bladder). If this blockage is incomplete or you still have functioning kidney on the other side then urine will still collect in your bladder and need to come out the usual way.