The difference between 'assault' and 'battery' is little more than a technicality. Here are the two legal definitions:
"An assault is committed when a person intentionally or recklessly causes another to apprehend the immediate infliction of unlawful force"
"A battery is committed when a person intentionally and recklessly applies unlawful force to another".
As you'll see, the wordings are fairly similar and they result in what is effectively the same charge (of either assault, or assault by battery, contrary to Section 39 of the Criminal Justice Act 1988).
From what you've written, the Crown Prosecution Service might find it hard to obtain a conviction and, even if they do, neither you not your partner should have much to worry about. While conviction for a 'Section 39' offence can theoretically result in a prison sentence (or up to 6 months, and/or a fine of up to �5000), such a penalty only ever results from the most serious of offences. (e.g. an offence close to the criteria for 'ABH', or perhaps an offence against a child). Unless your partner has a whole string of recent convictions for violence, the chances of him going to prison are absolutely NIL. If the CPS does succeed in obtaining a conviction, he'll simply receive a fairly small fine and/or a short period of community service. (Even a community service order is probably unlikely. A conviction would probably result in nothing more than, say, a �100 fine, plus �60 costs and a �15 payment to the victim compensation fund).
Chris