Hi, I am sorry to hear that you are having your third mc. It is a shocking and sad thing to go through :(
After my third mc they did the routine tests for genetic karyotyping, thrombophilia, hormones and thyroid levels and the health and shape of the uterus and ovaries via an internal scan. The genetic karyotyping is done for you and your husband to see if you are genetically similar.
This should all take about 3 months until you get test results.
Unfortunately, even with the all clear from the tests, I went on to miscarry a fourth time. It is very rare that they diagnose a problem with these tests, however, alot of women are diagnosed with blood clotting problems, which can cause miscarriages.
There are loads of other things you can be tested for privately, such NK cells - I am sure someone else here can give you more information on this.
The only advice I would like to give you is that, don't believe doctors when they say it's all due to bad luck. After my fourth mc, I don't believe luck has any part to play in this. Push the doctors to get tests - ask for repeats if necessary. I don't know if you have heard of St Mary's Hospital in London - it is the best Recurrent Miscarriage Clinic in the whole of the UK, so you may want to look into getting a referral there if you are in the south east.
I hope you find out what is causing the miscarriages - It is a horrendous thing to go through and it really scars you for life. Try to be positive and I know it's hard, but try to stay happy xx