Python for..else loop always triggers else

I am trying to read a tab-separated file and collect all characters except control characters. If a control character is hit, the remainder of line should be ignored too. I've tried the following code in Python 3.5, using a for..else loop:

import curses.ascii

input_file = ...
chars = set()
with open(input_file) as file:
    for line in file.readlines():
        source, target = line.split("\t")

        for c in source.strip() + target.strip():
            if curses.ascii.iscntrl(c):
                print("Control char hit.")
                break
            chars.add(c)
        else:
            print("Line contains control character:\n" + line)
            continue

        print("Line contains no control character:\n" + line.strip())

I'd expect this to check each character for being a control character and if it hits one (break is triggered), skip to the next line, hence trigger the else/continue statement.

What happens instead is that continue is always triggered, even if the break statement in the if clause is never reached for a line. Consequently, the final print statement is never reached either.

What am I doing wrong?