I see that this is a rather old post but just in case someone is still searching for a way to do this:
proc = subprocess.Popen(["ping", "localhost"],
stdout=subprocess.PIPE,
stderr=subprocess.PIPE)
with open("logfile.txt", "w") as log_file:
while proc.poll() is None:
line = proc.stderr.readline()
if line:
print "err: " + line.strip()
log_file.write(line)
line = proc.stdout.readline()
if line:
print "out: " + line.strip()
log_file.write(line)