Comparing a Binomial and Normal Distribution

So I'm currently analyzing several sets of data, that all represent the exact same type of data. There are multiple sets of this data, but however are in different forms. That is, some of this data is in the binary form, either presence of absence, while others are in the quantitative form. My main question, is whether it is appropriate to compare these two different types of data.
With the binary data, I was imagining that I would turn this into a percentage, and then use the binomial distribution to create a confidence interval. The quantitative data is already in percentage form, so with it, I'm able to create a normal distribution based on a t distribution. This has the classical confidence interval form, and I was wondering if it's possible to compare this normal distribution with the data generated from the binomial distribution. If this is possible, how do I do this, especially using something like R?
I was imagining that I would be able to do some sort of 2 sample t test with this data.