The direction of the fields of an electromagnetic wave is not conventional but it's determined by Maxwell's equations. For the particular case of a plane electromagnetic wave of angular frequency $\omega$ in vacuum, which can be represented by the picture you posted, Maxwell's equations require that the wave vector $\boldsymbol{k}$, the electric field $\boldsymbol{E}$ and the magnetic flux density $\boldsymbol{B}$ obey the relationships (the dot represent the scalar product and the cross the vector product)
$$\begin{align}&\boldsymbol{k}\cdot \boldsymbol{E} = 0, \\ &\boldsymbol{k}\cdot \boldsymbol{B} = 0, \\ & \boldsymbol{B}=\frac{1}{\omega}\boldsymbol{k}\times \boldsymbol{E}.\end{align}$$
This means that $\boldsymbol{k}$, $\boldsymbol{E}$ and $\boldsymbol{B}$ are three orthogonal vectors and that the direction of any one of them is determined by the other two. Therefore, no, you cannot mirror the magnetic field in the picture.
Note that if it were possible to mirror just the magnetic field, then, by superposition, you would be able to construct a wave having nonzero electric field but zero magnetic field.