This is another case where I believe Continental is engaging in breach of contract. Unfortunately this is becoming more and more common for Continental. For some reason, they seem to have lost their ethical footing within the last year.
I had a similar situation recently, and the only thing which finally got their attention was a small claims filing, which cost me $27.
I believe that the non-awarding of elite bonus miles is breach of contract, for several reasons: (i) the web site clearly says that Continental code-share flights operated by other carriers and ticketed as Continental qualify for the bonus - this is not an ambiguous statement and requires no further evidence to analyze its meaning - its plain on its face; (ii) in their course of dealing, Continental has previously awarded the bonus on these code-share flights. I have such evidence in printed form and would be willing to provide it to anyone who needs it to establish Continental's course of dealing at a small claims trial.
I believe the measure of damages here would be the lost mileage, calculated as a ratio of the average cost of the reward you intend to use the miles for. This is a significant and quantifiable number and something which you can caluclate and use in your claim.
The proper agent for service of process in California for Continental is:
Continental Airlines, Inc.
c/o CT Corporation Systems, Registered Agent
818 West Seventh Street
Los Angeles CA 90017
I believe that if anyone who is in this situation takes the time to file a claim, one of two things will happen. First, Contnental will call you and give you the miles in exchange for dismissing the suit or second, you will go to trial and you will win.
Continental has a strong above-the-law attitude lately - don't let them engage in breach of contract, call them on it. You are well within your rights to do so and have a very, very viable claim here.