You pretty much describe my own skills and experience. I bounced around filling in gaps by supervising and working in networking, programming, operations, and service desk. It gave me a respect for the specialist in each area, and a good understanding of all the areas.
We went through a long series of CIOs at a rate one every 10 months or so. When the last one made a public gaffe, they put me in at CIO on an interim basis. I been in the position about 75 months now.
All the problems that come up to me are based in two or more of the specific disciplines, otherwise the specialists would have solved it already. If you can understand the issues and explain the solution to CxO leaders and IT people, you'll do great.
Don't settle for just being a generalist in the IT areas, be a generalist in the business areas as well.