Based on this question : add minor gridlines to matplotlib plot using seaborn , you can do it like that.
sns.set_style("darkgrid")
fig, ax = plt.subplots(1, 1)
x = np.arange(10)
ax.plot(x, x)
ax.get_xaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())
ax.get_yaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())
ax.grid(b=True, which='major', color='w', linewidth=1.0)
ax.grid(b=True, which='minor', color='w', linewidth=0.5)
You obtain this figure :
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