Hi, I'd like to help you with your question.
It sounds like your husband is giving you a good reason to worry. The main reason is because he is putting his feelings and the secretary's feelings before yours. When he says he will not shun his secretary because of your fears, he is saying that she is more important than you are. In any marriage, for the relationship to grow and thrive, there needs to be a good base for trust, and this situation is taking away your ability to trust your husband. Also, the husband and wife must put each other first. From what you describe, this is not how your husband sees your marriage.
Yes, it is ok for men to be friends with women. But when a man is married, any female friendships he has must include his wife. In other words, they must be mutual friends. No married man should have any female friends that are sending cards to him at home nor should his focus be on making friends with every secretary he meets. That is inappropriate and suspicious behavior.
You have a right to stand your ground in your marriage and insist that your husband end his obsession with making friends with each of his secretaries. There is no reason he needs to be focused on secretaries when he is on a job site. He should be focused on his work instead.
Talk to your husband about seeking therapy together. He needs to understand his role in your marriage and you both need to work on how to handle this issue. To find a therapist, talk with your doctor for a referral. Or, if you attend church, talk with your pastor. Pastors and their staff are often very good in helping people with marital issues. You can also search on line at http://therapists.psychologytoday.com/rms/.
If your husband will not go to therapy, go without him. You need the support and help to figure out how you want to handle this situation.
Here are some resources to help you as well:
If You Think He's Cheating... He Probably Is! (How to Know if Your Suspicion is Right and What to Do When It Is) by Laura DeAngelo and Lara DeAngelo
My Husband's Affair Became the Best Thing That Ever Happened to Me by Anne Bercht
You can find these books on Amazon.com or your local library may have it for you.
I hope this helps you,