Is a data set considered to be linearly separable if it can only be separated by multiple hyperplanes?
In simple terms: Linearly separable = a linear classifier could do the job. You could fit one straight line to correctly classify your data.

Technically, any problem can be broken down to a multitude of small linear decision surfaces; i.e. you approximate a non-linear function with a high number of small linear boundaries. That's what Neural Networks are doing with ReLU activations btw, but nobody would say that Neural Networks are linear models.