This is basically doable.
Put the Earth in a standard 1 AU near-circular orbit around a binary pair (a P-type orbit, which I think is what you're asking after).
As long as the binary pair is less than about 0.22–0.40 AU apart, this should be reasonably gravitationally stable. This is 2–3 orders of magnitude larger than the Sun's Roche limit, so the Sun-like stars comprising the binary should not destroy each other or the planet tidally.
Ideally, the stars you pick would each mass half as much, and output about half the Sun's total illumination (slightly more to compensate, on average, for eclipses). Unfortunately, a star with half the mass of the Sun is expected to output just 8.83% of the light. You can compensate in various ways:
- Make the stars the same mass as the Sun, and move the orbit 41.4% outward to compensate (disadvantage: orbital period 18.9% longer; advantage: Sun-like light).
- Make the stars more massive and keep orbit the same (disadvantages: your orbit will be faster, light is red).
- Make the system about 30% the size, so you get enough light (disadvantages: shorter orbit, light is red).
- Changing the star types: e.g. perhaps a Sun-like star, and a nearly insignificant white dwarf (advantage: pretty similar in most respects, disadvantage: same)
You can generate innumerable other solutions (and similarly, if you use these numbers, you should check them, since I didn't). The main consideration is that irradiance (amount of power falling on surface) is 1/r^2 with distance. Formulae for orbital period, etc. are Google-able.
In short: there are lots of plausible ways to make an Earth-like planet around a binary. The main difficulty is finding star masses/luminosity/spectral class/orbital radius configurations that are similar to Earth's. It seems like either the year's length needs to change, or the amount of light or its spectral class needs to. On the other hand, this can also be a source of interesting difference in your story.