Preheat oven to 375 degrees F.
In a large bowl, mix together cornmeal, flour, sugar, baking powder and salt.
In a medium bowl, mix together eggs, buttermilk and oil until well combined.
Gently fold the liquid ingredients into the dry ingredients until just mixed. Take care not to overmix.
Add the drained cream corn, cheese and jalapenos to the batter. Gently fold in until just combined, taking care not to overmix.
Pour batter into a prepared baking pan (9 inch square or round is ideal). Smooth batter to evenly cover pan.
Bake for 20 to 25 minutes or until it starts to turn lightly golden brown around the edges and a toothpick inserted into the center comes out clean. Take care NOT to overbake as it will dry out the cornbread.
Remove from heat and allow to cool slightly prior to serving.