Do we say that we have a plolicy with a particular insurance company?

[tufguy]

Do we say that we have a plolicy with a particular insurance company? Like "I have a medical policy with life insurance company" or "I have had a life insurance policy with life insurance company for six years".

Is it also correct to say "I have an insurance with an insurance company"?

 

[PeterCW]

You would never say "an insurance".

In colloquial British English:
"I have medical / life insurance with company name". (Strictly it should be life assurance but everybody says insurance)
"I have had life cover with company name for six years" or "I have had life insurance with company name for six years".

In financial jargon your are "covered" by a policy so the word "cover" is sometimes substituted for "insurance".