The inscriptions are (note that the S's are backwards):
Obverse (bear) - MONETA BERNENSIS (coinage of Bern)
Reverse (cross) - SANCTVS VINCENCIVS (Saint Vincent)
(The style of lettering can be compared, with, for example, a 14th-century brooch shown here on page 2, also with reversed S's and closed-up E's; with a 1497 inscription showing A's with the same kind of top horizontal bar (though there it also has the interior one); etc. No doubt someone with greater expertise in medieval paleography could find better examples.)
It looks fairly similar to a coin shown at http://www.beastcoins.com/Topical/Bears/Switzerland/Bears-Switzerland.htm, under "Canton of Bern - 1400's." The size there about matches what you measured, and the description there says that it was a 5 Heller coin, and that its type is described in HMZ 167. (HMZ-Katalog, published in 1977 and reissued in 2006, is a standard reference for coins from Switzerland and Liechtenstein since the 1500s.)
I don't have the HMZ-Katalog, but this auction listing has the type as minted between 1492 and 1528.
In comments, LangLangC has found another listing that gives instead HMZ 166a and dates it still earlier, to 1400-1425. Someone with access to that catalog would have to take a look, then, and see which one this coin more closely resembles.
At any rate, it's quite a bit older than your father thought it was!