The function counts the number of digits in the input string when the input string includes both alphabetic and numeric characters and returns the count as a word. For other inputs, it returns an empty string.

[CODE]:
```python
def count_digits(input_string):
    digit_count = sum(c.isdigit() for c in input_string)
    if digit_count > 0 and any(c.isalpha() for c in input_string):
        return num2words(digit_count)
    else:
        return ""
```
Please note that the num2words function is not a built-in Python function and needs to be imported. It can be installed via the `num2words` package or replaced with a custom mapping of numbers to words.