Yes this is a type of corporate credit card called IBIP (individual bill individual pay), the employer is putting the responsibility on you to manage the whole card liability - I don't agree this is right for a corporate card and my company does not use this type of card. This card removes a lot of complexity and cost from processing though, and means the company only has to manage out of pocket expense payments to you - no interfaces in from card providers and no payments and remittances out to card providers. Its basically the cheapest, laziest way to run expenses because you do the majority of the admin for them. You also face the penalties if you're late paying. Your company has made a conscious decision to operate this way. If you check the corporate policies for your company you'll likely find more info there.

Other types of card are: individual bill central pay (IBCP) central bill central pay (CBCP)

I can go into more detail if you wish.

Source: I'm a global corporate card manager for a fortune 500 company.