Hi Jodyrae,
Welcome to SR, I am glad you found us but sorry for what brought you here.
There are many on SR who can relate to your story and most of us have arrived on SR because we had concerns for our loved ones health and wanted to help them.
Unfortunately, we soon learn that we cannot help our loved ones. They have to help themselves and want to and that is the real difficult part to accept.
The disease that is alcoholism, has some fundamental elements that you have already witnessed. You have expressed your concerns and was told not to worry. He is placating you but continuing drinking, because he cant stop. It doesn't matter how much you discuss with your BF how much you are worried for him and his health, it will not make a slight bit of difference. His urge to drink is so strong that nothing you do or say will make him stop.
Most of our 'functioning' alcoholics live in the strange world of denial. My AH doesn't think he is an alcoholic because he works, cooks and cleans. He also thinks that the term alcoholism was invented by the Americans so they can sell books. His denial allows him to continue drinking.
As you have discovered, the counseling your BF did failed in the long term. This is because an alcoholic has to stop drinking, they cannot simply cut down. Alcoholism is progressive and so one leads to two, leads to 3 etc, the need to drink is overwhelming for them.
When I found SR, I had no knowledge whatsoever about alcoholism and how it was affecting me. I was a mess, living with an alcoholic and worrying about him and wanting him just to stop drinking. My AH and I had many fights about his drinking and when I finally lost my patience and gave him a choice, he told me that he was choosing alcohol over me and a 22 year marriage.
This was my rock bottom and by chance someone told me to try Al-anon. Al-anon has been good for me and I am learning to live with my functioning alcoholic. I now understand that I didn't cause it, I cant control it and I cant cure it, but I continue to live with him and the very negative sides but do so whilst trying to protect myself and try to stay healthy in the mind, body and soul.
Alcoholism is known as a disease of the family, as it effects everyone who comes into contact with it, not only the drinker. You already sound conflicted and alcoholism will do this to you. You dont want your children to see this, you want a father figure for them, you love him.
Knowledge is power, so keep reading, check out some of the stickies above and check out a a local Al-anon group to you. Once you learn the facts/truths of alcoholism, and are able to keep the focus on you, it should help you to make clear, healthy decisions for you and your children, based on your own circumstances and what you can live with. Keep reading and posting and welcome again.