"Die beiden Frauen"
The spelling of "women" is admittedly very odd. I heard that, long ago, the person who decided to spell it that way owned a printing press and was considering "wimin" but decided that it would have too many vertical lines to read easily. Whether this is true or not, it's a story that illustrates that the spelling does not follow any conventional logic.
The endings of "beide" are the same as those for adjectives, i.e. among other things they depend on whether there is an article before the word "beide" or not: "Die beiden Frauen sind schön" vs. "Beide Frauen sind schön".
Background information on adjective endings: http://coerll.utexas.edu/gg/gr/index.html?si=adj