The company that employs me are offering me shares in the company. I pay in on a regular basis. I don't see anywhere about interest, but they will be subject to the market price of the company.
Are these shares halal?
Most Islamic companies do deal with shares, so it's halal. It is haraam if the company is selling haraam products, which I doubt is your concern if you're working for the company. So, I assume you're worried if it's Riba.
Riba is basically what happens when you lend someone a product at a fixed value and then request higher than the perceived value for it.
Trading is not Riba... for example, if you bought a sick cow, nursed it to health, sold it back at a higher price, that is halal.
But if you lent someone a sick cow and asked a healthy cow from him in return, it becomes Riba.
If you lent someone 10g of gold at $100, and got 10g of gold back at $300 later, it is not riba, because the value is different, just that the value of money (which is unrelated) has dropped. If you lent someone 10g of gold at $100 and got back 11g of gold worth $100, then that is Riba, because you are getting back more than the value.
In this case, if you're not lending or borrowed money, you shouldn't be worried about it. Even if the value was different, if you are not bound to return it, it should be considered trading.
Some scholars also consider dishonest trading as riba, like price fixing or hoarding goods.
Stocks are directly related to the value of your company and how many other people are owning those stocks. If you work hard for your company and the value goes up, it is a result of your work.
But if you are deceptively raising the prices through financial engineering, price fixing, or some insider information, like selling all your stocks when you know the CEO is going to step down, then the halalness of the money is questionable.
In general, shares or stock in a company that deals in permissible business or trading is permissible. Buy acquiring these shares you are investing your money in that company and acquiring part ownership. If the company does well, you profit. If it does badly, you sustain a loss. This is perfectly fine, and it's not riba since there is no guaranteed increase.
The two things to keep in mind however are that the business the company engages is must primarily be permissible according to shari'ah, i.e. among other things not engaged in trading unlawful things in Islam. The second thing is that most companies today invest their money in interest-bearing accounts in banks (or other interest-bearing vehicles). Since that also forms part of the profits of the company, it will affect your dividend. It is then upon you estimate how much of that income came from unlawful means and to proportionally remove it from your profit.
However bear in mind that more conservative scholars (not based in North America) opine that it is not permissible to own shares or stock in companies that deal with riba in their finances. http://www.islamqa.com/en/ref/45929/
I assume part of the discrepancy is due to the fact that in Islamic lands a company that deals with riba in their finances is (or should be) relatively rare whereas in the West it is extremely difficult to escape.
Reference: http://amjaonline.com/00en_f1_details.php?fid=79979 AMJA is a body of top North American scholars.
Muz has ignored the fact that the company should not be a in in dealing with haram transaction and also should not have at all (according to some scholars) or very little ( according to some scholars including Taki Usmani) interest paying debts.